An Ambrosetti–Prodi-type problem for the (p,q)-Laplacian operator

2019 ◽  
Vol 21 (01) ◽  
pp. 1750067
Author(s):  
Taísa Junges Miotto ◽  
Márcio Luís Miotto
Keyword(s):  
Existence Of Solutions ◽  
Laplacian Operator ◽  
Type Problem ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Continuity Result

This work has objective to obtain results of existence and multiplicity of solutions for an Ambrosetti–Prodi-type problem for the [Formula: see text] operator. Moreover, it was proved a continuity result for the parameter which limits the existence of solutions in relation of the parameter [Formula: see text].

scholarly journals On a Robin type problem involving 𝑝(𝑥)-Laplacian operator

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Abdesslem Ayoujil ◽  
Anass Ourraoui
Keyword(s):  
Variational Approach ◽  
Growth Conditions ◽  
Laplacian Operator ◽  
Robin Problem ◽  
Type Problem ◽  
Multiplicity Results ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Cerami Condition ◽  
Weaker Conditions

Abstract This paper deals with the existence and multiplicity of solutions for the p ⁢ ( x ) p(x) -Laplacian Robin problem without the well-known Ambrosetti–Rabinowitz type growth conditions. By means of the variational approach (with the Cerami condition), existence and multiplicity results of solutions are established under weaker conditions.

scholarly journals Multiple Solutions for a Nonlocal Elliptic Problem Involving p x , q x -Biharmonic Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Qi Zhang ◽  
Qing Miao
Keyword(s):  
Variational Principle ◽  
Elliptic Problem ◽  
Multiple Solutions ◽  
Sufficient Conditions ◽  
Biharmonic Operator ◽  
Type Problem ◽  
Navier Boundary Conditions ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Kirchhoff Type Problem

In this paper, using the variational principle, the existence and multiplicity of solutions for p x , q x -Kirchhoff type problem with Navier boundary conditions are proved. At the same time, the sufficient conditions for the multiplicity of solutions are obtained.

scholarly journals Existence of solutions for a family of polyharmonic and biharmonic equations

2005 ◽  
Vol 2005 (21) ◽  
pp. 3405-3417
Author(s):  
M. Hesaaraki ◽  
B. Raessi
Keyword(s):  
Boundary Condition ◽  
Bounded Domain ◽  
Existence Of Solutions ◽  
Existence Of Solution ◽  
Biharmonic Equations ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Fibering Method ◽  
Biharmonic Problems

We consider a family of polyharmonic problems of the form(−Δ)mu=g(x,u)inΩ,Dαu=0on∂Ω, whereΩ⊂ℝnis a bounded domain,g(x,⋅)∈L∞(Ω), and|α|<m. By using the fibering method, we obtain some results about the existence of solution and its multiplicity under certain assumptions ong. We also consider a family of biharmonic problems of the formΔ2u+(Δϕ+|∇ϕ|2)Δu+2∇ϕ⋅∇Δu=g(x,u), whereϕ∈C2(Ω¯), andΩ,g, and the boundary condition are the same as above. For this problem, we prove the existence and multiplicity of solutions too.

scholarly journals Existence of Solutions for a Robin Problem Involving thep(x)-Laplace Operator

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Mostafa Allaoui
Keyword(s):  
Variational Method ◽  
Boundary Value Problem ◽  
Laplace Operator ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Robin Problem ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

In this article we study the nonlinear Robin boundary-value problem-Δp(x)u=f(x,u)  in  Ω,|∇u|px-2(∂u/∂ν)+β(x)up(x)-2u=0on∂Ω. Using the variational method, under appropriate assumptions onf, we obtain results on existence and multiplicity of solutions.

scholarly journals Multiple solutions of boundary value problems on time scales for a φ-Laplacian operator

2020 ◽  
Vol 40 (4) ◽  
pp. 405-425 ◽  
Author(s):  
Pablo Amster ◽  
Mariel Paula Kuna ◽  
Dionicio Pastor Santos
Keyword(s):  
Boundary Value Problems ◽  
Time Scales ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Lower And Upper Solutions ◽  
Laplacian Operator ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

We establish the existence and multiplicity of solutions for some boundary value problems on time scales with a \(\varphi\)-Laplacian operator. For this purpose, we employ the concept of lower and upper solutions and the Leray-Schauder degree. The results extend and improve known results for analogous problems with discrete \(p\)-Laplacian as well as those for boundary value problems on time scales.

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